Year 4 Mathematics December 2011 Page 1 of 39 Mathematics Year 4 Mathematics -Student Portfolio Summary WORK SAMPLE PORTFOLIOS These work sample portfolios have been designed to illustrate satisfactory achievement in the relevant aspects of the achievement standard. The December 2011 work sample portfolios are a resource to support planning and implementation of the Foundation to Year 10 Australian Curriculum in English, Mathematics, Science and History during 2012. They comprise collections of different students’ work annotated to highlight evidence of student learning of different aspects of the achievement standard. The work samples vary in terms of how much time was available to complete the task or the degree of scaffolding provided by the teacher. There is no pre-determined number of samples required in a portfolio nor are the work samples sequenced in any particular order. These initial work sample portfolios do not constitute a complete set of work samples - they provide evidence of most (but not necessarily all) aspects of the achievement standard. As the Australian Curriculum in English, Mathematics, Science and History is implemented by schools in 2012, the work sample portfolios will be reviewed and enhanced by drawing on classroom practice and will reflect a more systematic collection of evidence from teaching and learning programs. THIS PORTFOLIO – YEAR 4 MATHEMATICS This portfolio comprises a number of work samples drawn from a range of assessment tasks, namely: Sample 1 Fractions – Fraction cards Sample 2 Comparing and ordering fractions Sample 3 Financial mathematics – Hermit crabs Sample 4 Location – Using maps Sample 5 Transformation – Area of 10 squares Sample 6 Time and measurement – Planning with a calendar Sample 7 Numbers – Multiplication and division strategies Sample 8 Numbers – Chocolate boxes Sample 9 Units of measurement – How many days? Sample 10 Data representation and interpretation – Collecting, graphing and interpreting data - gold Sample 11 Chance – Chance words Sample 12 Geometric reasoning – Right angles
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Year 4 Mathematics December 2011Page 1 of 39
Mathematics
Year 4 Mathematics -Student Portfolio Summary
WORK SAMPLE PORTFOLIOS
These work sample portfolios have been designed to illustrate satisfactory achievement in the relevant aspects of the
achievement standard.
The December 2011 work sample portfolios are a resource to support planning and implementation of the Foundation to
Year 10 Australian Curriculum in English, Mathematics, Science and History during 2012. They comprise collections of
different students’ work annotated to highlight evidence of student learning of different aspects of the achievement standard.
The work samples vary in terms of how much time was available to complete the task or the degree of scaffolding
provided by the teacher.
There is no pre-determined number of samples required in a portfolio nor are the work samples sequenced in any
particular order. These initial work sample portfolios do not constitute a complete set of work samples - they provide
evidence of most (but not necessarily all) aspects of the achievement standard.
As the Australian Curriculum in English, Mathematics, Science and History is implemented by schools in 2012, the
work sample portfolios will be reviewed and enhanced by drawing on classroom practice and will reflect a more
systematic collection of evidence from teaching and learning programs.
THIS PORTFOLIO – YEAR 4 MATHEMATICS
This portfolio comprises a number of work samples drawn from a range of assessment tasks, namely:
Sample 1 Fractions – Fraction cards
Sample 2 Comparing and ordering fractions
Sample 3 Financial mathematics – Hermit crabs
Sample 4 Location – Using maps
Sample 5 Transformation – Area of 10 squares
Sample 6 Time and measurement – Planning with a calendar
Sample 7 Numbers – Multiplication and division strategies
Sample 8 Numbers – Chocolate boxes
Sample 9 Units of measurement – How many days?
Sample 10 Data representation and interpretation – Collecting, graphing and interpreting data - gold
Sample 11 Chance – Chance words
Sample 12 Geometric reasoning – Right angles
Year 4 Mathematics December 2011Page 2 of 39
Mathematics
Year 4 Mathematics - Student Portfolio Summary
This portfolio of work shows the creation of pairs of equivalent fractions when working with halves, quarters, thirds and
fifths, location of halves and quarters on a number line and identification of equivalent fractions in this context (WS1,
WS2). The student understands the value of a fraction can also be represented as a decimal and identifies fractions
equivalent to 0.5 (WS2). The student recalls multiplication and division facts to 10 X 10 and demonstrates an ability to
solve simple purchasing problems (WS3) and simple time duration problems (WS3). The student interprets maps and
compiles directions (WS4) using appropriate directional language and compares areas of regular and irregular shapes
and understands line symmetry (WS5). The student converts between weeks and days and between hours, minutes
and seconds (WS6, WS9), identifies and classifies angles which are smaller than, equal to or greater than a right angle
(WS12) and identifies a straight line as a half turn. The student collects and displays data and lists the probabilities of
everyday events (WS10, WS11).
The following aspects of the achievement standard are not evident in this portfolio:
Students have been using fraction kits to investigate equivalent fractions. As yet they have had no explicit teaching
about equivalent fractions and decimals.
In groups, students were given a set of fraction cards where the fractions had denominators 2, 3, 4, 5, 6, 8 and 10.
They were asked to record each fraction as a decimal and a percentage.
Students displayed their recordings and shared their findings with the class.
Variation: The fraction cards could contain multiple representations of the same fraction, for example 50%, 0.5.
Students could use these cards to play Concentration, Snap, or Old Maid.
Year 4 Mathematics - Work sample 1
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Mathematics
AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Students have been given opportunities to make halves, quarters, eights, thirds and fifths. They have been
investigating equivalent fractions using fraction walls.
The teacher prepared a series of fraction cards as follows:
Students were asked to place the cards on a number line. Students were encouraged to discuss the correct placement
of the cards and why some cards need to be placed on top of other cards.
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Year 4 Mathematics - Work sample 2
Work sample 2: Comparing and ordering fractions
AcknowledgementACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Annotations
Locatesandordersfractionsonthenumberline.
Recognisescommonequivalentfractions.
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Year 4 Mathematics - Work sample 3
Work sample 3: Financial mathematics – Hermit crabs
Work sample 3: Financial mathematics – Hermit crabs
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Mathematics
AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
After using informal units to compare areas of shapes, students had begun to use square units. Students have been
discussing line symmetry in their work on shape.
Students used grip paper to construct shapes with an area of 10 square units and patterns or pictures with 10 square
units shaded.
Students were asked to identify lines of symmetry on their patterns and shapes.
Year 4 Mathematics - Work sample 5
Year 4 Mathematics December 2011Page 17 of 39
Year 4 Mathematics - Work sample 5
Mathematics
AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Work sample 6: Time and measurement – Planning with a calendar
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Mathematics
AcknowledgmentACARA acknowledges the contribution of the Queensland Studies Authority for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Students have been given opportunities to use their recall of multiplication and division facts.
Students have discussed the use of brackets but have not discussed order of operations.
Students were asked to select 15 numbers between 1 and 100. They were to express each of the selected numbers in
two different ways using mixed operations. Each operation was required to include either a multiplication or a division.
Year 4 Mathematics - Work sample 7
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AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Students have been learning to use their times tables and related division facts.
The teacher posed the problem: ‘Imagine you had the job of designing a chocolate box. There are to be 48 chocolates
in the box. The box can be one or two layers high. How many ways could you arrange the chocolates in the box?’
Students drew or made models of their solutions and discussed these in terms of multiplication and division facts.
Year 4 Mathematics - Work sample 8
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AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Students have been using calculators to solve problems involving the four operations.
The teacher posed the problem ‘How many days have you attended school this term/year?’ Students calculated a
solution.
Students were asked ‘How many other ways can you express this information?’, for example in hours, in minutes.
Students used a calculator to check their answers.
This activity could be extended by asking ‘How many hours have you spent at recess and lunch this week?’ Students
could record information in days, hours or minutes on a spreadsheet and then draw a graph.
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Year 4 Mathematics - Work sample 9
AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
In this task students compared and observed expected frequencies and communicated probabilities. The students
were given 30 minutes to complete this task.
Students completed a data collection task using gold panning. The activity involved students taking a small handful
of counters from a bag 7 times, which represents 7 days’ findings on the goldfields. Yellow counters represent a set
amount of gold (in grams). Students completed a graph or table to show their knowledge of collecting data and creating
a graph. Students then explained their findings.
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Year 4 Mathematics - Work sample 10
AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Students have discussed language that can be used to explain events of chance.
Students were given the following chance words on cards: always, never, sometimes, often, might, equal chance,
probably, certain, possible, and mostly.
In groups, students were asked to order them on a number line from 0 (impossible) to 1 (certain). Students compared
their order with other groups and discussed. They then matched each word with an everyday event, for example ‘We
sometimes play tips at lunchtime.’ There is an equal chance it will rain tonight.’
The student scribed these sentences to this scale:
a) It is certain I am at school today
b) I often watch t.v.
c) I will probably eat my dinner before 6pm
d) I sometimes don’t eat breakfast
e) I might be a Policeman when I get older
f) I will never be 5 years old again.
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AcknowledgmentACARA acknowledges the contribution of the NSW Department of Education and Communities for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.
Work sample 12: Geometric reasoning – Right angles
Year 4 Mathematics - Work sample 12
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Annotations
Identifiesastraightedgeasgreaterthanarightangle.
Work sample 12: Geometric reasoning – Right angles
Year 4 Mathematics - Work sample 12
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Mathematics
AcknowledgmentACARA acknowledges the contribution of trial school teachers and students for providing the tasks and work samples. The annotations are referenced to the Australian Curriculum achievement standards.